I understand the Maths.
The issue is that rotation prevents players from gaining momentum and in turn will probably hinder the development of certain players. Looking at it logically, when everyone was fit in Jan, Aguero couldn't get a game. Add in Sanchez and Silva and you have a problem. I'm aware that Navas and Nolito have moved on but I'd seriously question if either player would ever be good enough go stake a claim based on merit.
My point is simple. If you decide to throw 130m at 3 young attackers, let them play and develop. Back them to succeed. Don't block their path by signing players who will play ahead of them.
Name me a top side who can rotate 8-9 players for 4-5 positions whilst maximising the development of their young players and maintaining the harmony of the older players. Hasn't worked at Real, hasn't worked at Bayern.
Bringing up Real isn't a very good point, they had 10 players fighting for 5 spots (Ronaldo, Benzema, Bale, Vasquez, Asensio, Isco, James, Morata, Modric, Kroos), so it's not too surprising some players aren't happy with their game time. James is unhappy because he simply doesn't fit into Zidane's plans, and the number of players they have also affords them an injury (to Bale for example) and continue going on with no dips.
Here would be the very realistic bad scenario for example, if we have 3 wingers in 2 spots (B Silva, Sane, Sterling) and 1 get's injured, then the other 2 players have to play EVERY game after and will suffer due to exhaustion, this is inadequate depth, not to mention that B Silva would also play CM as well. You could say well maybe Kevin can step in to rotate with the wingers, but that is clearly not ideal.
Now if you have 4 wingers in 2 spots, then if an injury happens to one winger, you have 3 who can still rotate effectively. If our 4 wingers have perfect non-free injury seasons, then first of all that's great, but the amount of games is not as little as you think, atleast 28 games next season is still very good for the development of Sane and Sterling, 2 wingers who were CLEARLY gassed out last season due to Pep's over reliance.
Edit: This is why I wanted you to say explicitly what you meant and I brought up the maths, because you keep saying they won't get enough games for development and then don't say what you think is an acceptable number of games to play in a season. I think playing 28 (over 2500 mins) full games would be decent for a young 21 year old winger for example.
Edit2: To clarify, I still don't want Sanchez for depth even though it seems I'm arguing for him. I'm really arguing for SOMEBODY for depth, and in my opinion that should go to Patrick Roberts. That will give us 4 wingers spots, with B Silva also playing CM so not really being a full winger